Fox’s new sitcom “Ben & Kate” is about that rarely explored relationship: the brother and sister, that lifelong bond that can be by turns frustrating, inconvenient and yet unexpectedly moving. The laughs are built-in: Well-meaning troublemaker Ben (Nat Faxon) moves in with his younger sister, Kate (Dakota Johnson), a single mom who doesn’t need any more responsibilities; she has a 5-year-old. Creator Dana Fox sees plenty of emotional potential amid the laughs.

“It’s such rich territory,” says Fox. “Any time we want to talk about why they’re doing something ridiculous, you can flash back to them as kids. And on the fun side, they feel like a married couple griping at each other because they’ve known each other for 25 years.”

The series is based on Fox’s relationship with her older brother Ben. In working as a producer on her friend Liz Meriwether’s show “New Girl” last year, Fox, who’d previously written for the movies (“The Wedding Date,” “What Happens in Vegas”), learned the benefit in creating a series from what you know.

“She said, ‘It has to be personal, because you have to be able to write 100 episodes about it. So it better be in your blood,’” Fox says.

The trick, though, was not making the TV Ben willfully ridiculous. That’s not what you would call someone who, according to Fox, started eating her husband’s birthday cake on the way to her house because he couldn’t resist her baking skills. Or who, when Fox was a Stanford undergrad, showed up on campus, convinced her to vacate her dorm so he could live there for two months, and wormed his way into the elite college’s career center and took job-interview spots from no-show Stanford students.

The real Ben Fox is now in online advertising, has two children, and is “the best father,” says his sister — the show, however, will cover the pre-responsible Ben.

Of the character she created, Fox says, “He’s always making a plan. It might be an ill-conceived plan” — the pilot depicts a romantically despondent Ben scheming to crash his ex-girlfriend’s wedding — “but he’s going to do it with so much heart and gusto that even if it goes terribly awry, you’re not mad and you had a good time. My brother, when I really need him, he comes through.”

Casting Ben highlighted the difficulties in capturing the role’s nuances. Says Fox, “Certain guys would play it too mean. There’s not a mean bone in his body. But when they were playing it nice, it wasn’t edgy enough. And when they were playing it funny, it wasn’t heartfelt.”

Enter Faxon, a go-to bit player for “Ben & Kate” pilot director Jake Kasdan (“Bad Teacher”), a reliably funny improv actor, and someone whose sweet-faced mug rests easily in that space between haplessness and cluelessness. Faxon quickly took to the idea that people could laugh at Ben, but also root for him.

“It’s sort of freeing to play somebody who has a super-positive outlook on everything that comes his way without worrying about stresses like a job, or having to make a certain amount of money,” says Faxon. “Doing the things he does, he doesn’t feel they’re out of control or abnormal or silly.”

Thankfully, when it came time to convince the network that Faxon was the only possible Ben, the actor’s other career — screenwriting — simultaneously struck gold: Faxon and writing partner Jim Rash’s script for “The Descendants,” co-written with Alexander Payne, had just won the Academy Award for Best Adapted Screenplay.

Explains Fox, “Literally the weekend after he won the Oscar, we went in on Monday and said ‘Will you hire this guy?’ And they were like, ‘Yes we will!’”

When asked if he’ll need to wield his statuette on set, Faxon jokes, “If necessary, it will come out.”

It certainly proved handy on Oscar night, he says, when he arrived at the Vanity Fair party with a group that had swollen to 12 friends, family members and colleagues, and by holding his Oscar out the car window, got everybody in. “It was the coolest thing,” he says. “It was like a free pass.”

The real Ben Fox’s all-access ways are more mysterious, however. His sister recounts last spring’s network upfronts in New York, when her big brother flew in unannounced and somehow got inside the Fox network’s ticket-only presentation at the Beacon Theatre.

Dana Fox recalls sending the network’s then-programming chief Kevin Reilly an e-mail afterward: “It said, ‘Thank you. You’re so kind to the show, and if you think my brother didn’t crash the upfronts, you’d be sorely mistaken.’ He wrote back, ‘And if you think your brother wasn’t with me at a party you weren’t invited to, you would be sorely mistaken.’ I was like, ‘Perfect.’”